2 Answers
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All Intel Core 2 Duo and Intel Core i3, i5 and i7 support either 32 Bit or 64 bit. You will not have a problem with this. With what you might have a problem is with the amount of memory you need. For 32 Bit the minimum for a good running system is 512MB, the maximum is 4GB. For 64Bit the minimum recommended is 2GB and the maximum is "let your imagination fly!!!". I have tested 64Bit versions on 1GB and they can run very slow sometimes. The more memory the better.

If your Core 2 Duo laptop has at least 4 GB of ram I would recommend 64 bit but since it is a laptop and the more memory you have in a 64 bit the better, I would recommend sticking with the 32 Bit version. You actually don't loose to try both but for your case I would go more with the 32 Bit version (Except if it is some kind of 4GB+ Ram Laptop).